Festive Fractals

I delivered a festive online session for Potential Plus UK in which I introduced participants to the idea of mathematical fractals. It includes a demonstration and instructions for creating your own fractal Christmas card.

View it in the player below - there's still time* to make your own and post to family and friends!

*Unless, of course, there isn't.

Mathematics in work: Energy & Environment Project Coordinator

As part of Cambridge Mathematics' Interviews and Intersections series, Energy & Environment Project Coordinator Zoe is interviewed about her work and life, and the place of mathematics within them.

Click below to read the post and then join the conversation on Twitter here!

Intersections: Mathematics and the energy & environment project coordinator

What are the Chances? Lucky Tourist Cracks Safe Code

Image by Sergei Tokmakov, Esq. from Pixabay

Prompted by an article with a very similar headline, this post at the link below looks at exactly how likely the situation in the article - a person guessing the correct combination to a specific safe first time - is:

What are the Chances? at tommaths.blogspot.com

How Was 𝜋 First Calculated?

The Greek letter 𝜋 ("Pi", pronounced - at least in the UK - like "pie") when encountered in mathematics is usually used as shorthand for a pretty important number. This number can be defined in various ways, but arguably the simplest is "the ratio of a circle's circumference to its diameter." To put it another way, 𝜋 tells you how many times bigger the circumference is than the diameter; or it's the number you get if you divide a circle's circumference by its diameter:

\[ \pi = \frac{C}{d} \]

Circumference, Diameter & Pi by T.Briggs is licensed under CC BY-SA 4.0

One way that 𝜋 could be calculated is by measuring the diameter and circumference of a given circle and dividing the latter by the former. But one of the reasons we might want to know a value for 𝜋 in the first place is that it is difficult to measure the circumference of a circle.

Big Ben Strikes Again

Big Ben (well, its tower, lit up at night) Photo via Good Free Photos

This piece of Actual Maths concerns the third episode of the original Captain Scarlet TV series, Big Ben Strikes Again. You can watch it online via Amazon Prime, buy it on DVD, or probably find it elsewhere if you do some Googling. Maybe you've got a dusty old DVD lying around somewhere already or, if you're really retro, a video.

I loved watching repeats of Thunderbirds, Stingray and Captain Scarlet when I was growing up, but the first time I heard about this lovely example of Actual Maths was as the subject of a talk by Matthew Scroggs at Big MathsJam.

If you want to watch the episode before risking spoilers you'll probably want to stop reading about here and come back when it's finished.

The Cube

A 14 minute podcast exploring the most basic of 3D shapes, the cube, exploring where they turn up in our modern world, why they aren't used more and what one looks like in four dimensions!

Marcus du Sautoy's Five Shapes: The Cube

De-wobbling Tables

Helen sent me this:

I'm not sure where this originated, so apologise for the lack of a reference. I'll happily update if someone can point me in the right direction! In the mean time I'll just link to the tweet I was sent.

I've heard this before: if you're suffering from a wobbly four-legged table don't mess around with trying to fold a napkin or stack beer mats to just the right thickness. Instead just turn the tables on that problem by... turning the table. Twist it around its own axis of symmetry and, within a quarter turn, you'll have a stable table.

There's a reason why this works and one of the places you can find out about that is in the Numberphile video embedded below:

What's the Point of... Inequalities?

A poster introducing some uses of inequalities:

This is a reduced-quality image. Download the full-resolution poster at the link below.

What's the point of... Inequalities?

What's the point of... Imaginary Numbers?

A poster detailing some of the uses of imaginary numbers:

This is a reduced-size image. Download the full-resolution poster at the link below.

What's the point of... Imaginary Numbers?

What Do the Percentages Mean on Steep Road Warning Signs?

Maths teacher Simon Young tweeted a thread about percentages on road signs, and he's given me permission to write it up as a blog post. I've stayed faithful to Simon's original wording, with a little editing here and there, mostly based on his own corrections and some of the conversation resulting from his thread (the original thread is linked at the end).

Road steepness is expressed as a percentage on UK road signs: what does it mean, and where do the numbers come from?

Have you ever wondered what the percentages mean in those road signs about an upcoming gradient change? I know I have! Here is what I discovered...

What's the point of... Graphs?

A poster describing some of the uses of graphs:

This is a reduced-quality image: download the full-resolution version at the link below.

What's the point of... Graphs?

The Maths of Pointless

How often do we come up against people who are convinced that mathematics is pointless? TV game show Pointless requires contestants to obtain the lowest score to win against their opponents. Plus magazine discusses the maths behind this idea in two articles. The first looks at luck and unluckiness in TV game shows (with reference to Pointless); the second looks at some of the more general mathematical ideas related to Pointless specifically.

1. Pointless: The maths of TV gameshows

2. A Pointless return!

What is a Black Hole?

Over at Plus Magazine, this interview discusses what black holes are and how to describe them mathematically.

What is a Black Hole - Mathematically?

You can also find out more about black holes at Blogstronomy! 

What's the point of... Geometry?

A poster suggesting some of the uses of geometry.

This is just a thumbnail: click the image or use the link below to download a high-resolution version from the originator.

What's the point of... Geometry?

What's the point of... Exponentials?

A poster introducing some of the uses for exponential functions.

This is just a thumbnail: download the full-resolution version at the originator's website (click on the image or the link below).

What's the point of... Exponentials?

What's the point of... Distributions?

A poster introducing some of the uses for statistical distributions.

This is just a thumbnail: click the image or the link below to download the full-resolution version from the originator's website.

What's the point of... Distributions?

What's the point of... Differentiation?

A poster presenting some of the uses of differentiation.

This is just a thumbnail: click the image or the link below to download the full-resolution version from the originator's website.

What's the point of... Differentiation?

What’s the point of... the Binomial Theorem?

A poster presenting some of the uses of the Binomial Theorem.

This is just a thumbnail: click the image or the link below to download a full-resolution version from the originator's website.

What's the point of... The Binomial Theorem?

What's the Point of... Algebra?

A poster presenting just a handful of uses of algebra.

This is just a thumbnail: click on the image or the link below to download the full-resolution version from the originator's website.

What's the Point of... Algebra?

What’s the point – Aerial Photography

Free printable posters discussing some of the mathematics represented in a photograph of a street performer.

This is just a thumbnail: Click the image or the link below to download the full poster from the originating site!

What’s the point – Index Jump

Mathstonbury

Some maths teaching activities based on Glastonbury! This is a lot more contrived than much of the stuff I try to link to on here, but having been part a festival committee many moons ago the general idea of some of these is close to bits of the reality.

Mathstonbury at Mathmaticow.com

Space Maths: Teaching Resources

STEM Learning play host to a collection of teaching resources from the European Space Education Resource Office:

ESERO & STEM Learning: Space Teaching Resources: https://www.stem.org.uk/esero/resources

How to Draw an Ellipse

As part of an online session on Kepler's 1st & 2nd laws I described how to draw an ellipse using two pins, a pencil, and a loop of string. The participants asked for some instructions that they could use after the session, so here they are:

Hawking Radiation

There's plenty of maths in various areas of physics. Click below for a quick post explaining our understanding of Hawking radiation and its roots in mathematics.

Maths in a Minute: Hawking Radiation: https://plus.maths.org/content/maths-minute-hawking-radiation

And find out more about black holes at Blogstronomy! 

Squashing the Curve: Pandemic Modeling

Towards the beginning of 2020's Covid-19 outbreak there was much talk about "flattening the curve" to reduce strain on medical services. This article, published in March, compares English government plans released at the time with an early study by Imperial College, London.

Squashing the curve? https://plus.maths.org/content/how-best-deal-covid-19

Maths as a Developer

Contrary to most experiences in internet-land, the comments are where to go for the meat of this discussion on Luke Garrigan's post asking where programmers and developers use mathematics. There are a broad variety of responses from

"we're doing a huge disservice to our CS students by teaching so much math,"

through

"I expect there's a fair bit of it around, it's just not acknowledged as such,"

to

"Even when most of the work I'm doing comes from an external library an understanding of the math behind the functions is the difference between success and frustrating failure."

Check it out at the link below. Maybe some of you will have experiences of your own to contribute so please do join in with the discussion!

Do you actually use maths as a developer? https://dev.to/lukegarrigan/do-you-actually-use-maths-as-a-developer-24cc

A Partition Enigma

Colin answers a question on partitioning numbers, prompted by an aspect of Enigma codebreaking discussed in Dermot Turing's book, X, Y & Z: The Real Story of How Enigma Was Broken.

Ask Uncle Colin: A Partition Enigma: https://www.flyingcoloursmaths.co.uk/auc_enigma-md/

Could You be a Codebreaker?

A short set of activities designed to demonstrate a range of skills required by Bletchley Park's codebreakers, highlighting the intersection of a number of mathematical skills with things that are often not thought of as being mathematical (but very definitely are!)

#TheBletchleyParkChallenge 18 ⚙️ - Could you be a Codebreaker?

Take a look at the list at the beginning of this activity sheet ⬇️ https://t.co/e5ZAPExfUI

Which skills do you already have? Which ones do you need to work on? pic.twitter.com/ldPRLcoVIX

— Bletchley Park (@bletchleypark) May 16, 2020

Make Your Own Enigma Machine

The history of cryptology is one that is rife with examples of mathematics, with a significant burst of advancements in the first half of the 20th Century. An iconic player in this period is the Enigma machine,  arguably the most famous cryptographical device ever whilst also being the subject of many an varied misunderstandings and misconceptions. Where better to start understanding it, and its place in mathematical history, than by building a physical emulator of your own...

#TheBletchleyParkChallenge 12 - Build and learn to use your own Crisp Tube Enigma machine! ⚙️

Instructions and printables can be found here ➡️ https://t.co/VT9iXCCRhT

Share your creations with us! 🔎 #MuseumFromHome pic.twitter.com/PQLwZArIbW

— Bletchley Park (@bletchleypark) May 2, 2020

... and comparing it to the real thing?

#TheBletchleyParkChallenge 12 - Build and learn to use your own Crisp Tube Enigma machine! ⚙️

Instructions and printables can be found here ➡️ https://t.co/VT9iXCCRhT

Share your creations with us! 🔎 #MuseumFromHome pic.twitter.com/PQLwZArIbW

— Bletchley Park (@bletchleypark) May 2, 2020

Make a Caesar Wheel

The Caesar shift cipher was an early method of encrypting information and is often used as an entrypoint to the world of cryptography, cryptanalysis and cryptology, which is itself an inherently mathematical discipline.

#TheBletchleyParkChallenge 02 - Make a Caesar Wheel and try encrypting your own messages ⚙️

Here's your very own Bletchley Park template and a how-to guide ➡️ https://t.co/7LdL5fKK6m

Try encrypting some messages and send them to family and friends! ✉️

— Bletchley Park (@bletchleypark) April 9, 2020

The above challenge was followed a few days later by a further, related challenge:

#TheBletchleyParkChallenge 09 ⚙️ - Make your Caesar Wheel messages harder to break!

If you have a Caesar wheel and know how to use it (see day two’s challenge!) you can make messages harder to break by using a key word (rather than just one shift).https://t.co/Fbl5c0Hb9j

— Bletchley Park (@bletchleypark) April 25, 2020

Life Stats

Enter your date of birth and read some interesting statistics about the world since you came into it. Plenty of discussion starters here!

Life Stats:

https://neal.fun/life-stats/

Venus Transits and the Size of the Solar System

This entry in 2020's Big Lock-Down Math-Off hosted by the Aperiodical introducess the Venus transits of the 1600s and their importance in developing an early understanding of the true scale of our Solar system (when the page loads, scroll about half way down to find the article).

Venus Transits and the Size of the Solar System: https://aperiodical.com/2020/05/the-big-lock-down-math-off-match-23/

And you can find out more about Venus at Blogstronomy! 

American Football and Maths

Ex- professional American Footballer John Urschel is studying for a PhD in mathematics. In this Numberphile podcast he discusses his interest and career in both, touching on some of the crossovers between two disciplines many people would assume to be entirely separate.

Mathematical Quotes

Around 400 quotes about mathematics and from mathematicians, collated by Colin Beveridge of Flying Colours Maths.

Mathematical Quotes: https://www.flyingcoloursmaths.co.uk/mathematical-quotes/

100 (ish) of these are available for purchase as an ebook for Amazon Kindle: https://amzn.to/3h0DVhv

Music and Maths: The Score

This episode of the Relatively Prime maths podcast explores just a small part of the intersection between mathematics and music. 

ACMEScience · Relatively Prime: The Score

Mathematics and Medicine: AI & Metabolites

Maths fan and Biotech entrepreneur  Leila Pirhaji shares her plan to build an AI network to improve understanding and treatment of disease. See her TED talk in the player below or find further details, a transcript and further reading on the TED website.

Social Distancing Rules: Bad Maths

In June 2020 the world was dealing with the Covid-19 pandemic and "social distancing" was a buzzword for the time: everyone had to stay a given distance away from each other to reduce the chances of catching the virus or passing it on to someone else. There was much debate as to what this distance actually should be and, in the lead up to the potential reopening of shops in the UK, on 5th June The Guardian published this article:

One of the illustrations from the Guardian article

Plans to reopen shops in England 'in chaos' over social distancing rules

Study finds 10 sq metres of space is required per shopper to stick to government’s 2-metre guidelines

Link: https://www.theguardian.com/business/2020/jun/05/shops-reopen-england-social-distancing-rules-coronavirus

Maths teacher Mark Dawes found the original source for the mentioned study and wrote a critical piece about it and the article linked above, discovering and explaining some of the misconceptions and mistakes spanning both:

More than sums (blog) - Mathematically Distant: https://morethansums.blogspot.com/2020/06/mathematically-distant.html